H. Freeman – Communications of the ACM

Research and Advances Jun 1 1979

The cyclic order property of vertices as an aid in scene analysis

A cyclic-order property is defined for bodies bounded by smooth-curved faces. The property is shown to be useful for analyzing pictures of such bodies, particularly when the line data extracted from the pictures are imperfect. This property augments previously known grammatical rules that determine the existence of three-dimensional bodies corresponding to given two-dimensional line-structure data.

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Research and Advances Jul 1 1975

Determining the minimum-area encasing rectangle for an arbitrary closed curve

This paper describes a method for finding the rectangle of minimum area in which a given arbitrary plane curve can be contained. The method is of interest in certain packing and optimum layout problems. It consists of first determining the minimal-perimeter convex polygon that encloses the given curve and then selecting the rectangle of minimum area capable of containing this polygon. Three theorems are introduced to show that one side of the minimum-area rectangle must be collinear with an edge of the enclosed polygon and that the minimum-area encasing rectangle for the convex polygon is also the minimum-area rectangle for the curve.

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